What is the integral of (cos(pi/(x^{41)}))/(x^{42)} ?

The integral of (cos(pi/(x^{41)}))/(x^{42)} is -1/(41pi)sin(pi/(x^{41)})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (cos(pi/(x^{41)}))/(x^{42)}

\int \frac{cos ( \frac{π}{x ^{41}} )}{x ^{42}} d x

- \frac{1}{41 π} sin (\frac{π}{x ^{41}}) + C

Solution steps

\int \frac{cos ( \frac{π}{x ^{41}} )}{x ^{42}} d x

Apply u-substitution

: \int \frac{cos ( \frac{π}{u} )}{41 u ^{2}} d u

= \int \frac{cos ( \frac{π}{u} )}{41 u ^{2}} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{41} \cdot \int \frac{cos ( \frac{π}{u} )}{u ^{2}} d u

Apply u-substitution

: \int - \frac{cos ( v )}{π} d v

= \frac{1}{41} \cdot \int - \frac{cos ( v )}{π} d v

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{41} (- \frac{1}{π} \cdot \int cos (v) d v)

Use the common integral:

\int cos (v) d v = sin (v)

= \frac{1}{41} (- \frac{1}{π} sin (v))

Substitute back

= \frac{1}{41} (- \frac{1}{π} sin (\frac{π}{x ^{41}}))

Simplify

\frac{1}{41} (- \frac{1}{π} sin (\frac{π}{x ^{41}})) : - \frac{1}{41 π} sin (\frac{π}{x ^{41}})

= - \frac{1}{41 π} sin (\frac{π}{x ^{41}})

Add a constant to the solution

= - \frac{1}{41 π} sin (\frac{π}{x ^{41}}) + C

\int ln (y^{2}) d y

x \to 1 - lim (\frac{2 - x}{x - 1})

x \to \infty - lim (\frac{( 8 x ^{3} + 6 x + 7 )}{( 6 x - 7 )})

f (x) = \frac{x + 3}{2}

\int x^{2} (2 x - 4)^{5} d x

What is the integral of (cos(pi/(x^{41)}))/(x^{42)} ?
The integral of (cos(pi/(x^{41)}))/(x^{42)} is -1/(41pi)sin(pi/(x^{41)})+C